Lesson 13

Select all expressions that are equal to \(3 \boldcdot 3 \boldcdot 3 \boldcdot 3 \boldcdot 3\).

\(3 \boldcdot 5\)

\(3^5\)

\(3^4 \boldcdot 3\)

\(5 \boldcdot 3\)

\(5^3\)

Noah starts with 0 and then adds the number 5 four times. Diego starts with 1 and then multiplies by the number 5 four times. For each expression, decide whether it is equal to Noah’s result, Diego’s result, or neither.

1. \(4 \boldcdot 5\)
2. \(4+5\)
3. \(4^5\)
4. \(5^4\)

Decide whether each equation is true or false, and explain how you know.

1. \(9 \boldcdot 9 \boldcdot 3 = 3^5\)
2. \(7 + 7 + 7 = 3 + 3 + 3 + 3 + 3 + 3 + 3\)
3. \(\frac{1}{7} \boldcdot \frac{1}{7} \boldcdot \frac{1}{7} = \frac{3}{7}\)
4. \(4^1 = 4 \boldcdot 1\)

5. \(6 + 6 + 6 = 6^3\)

1. What is the area of a square with side lengths of \(\frac35\) units?
2. What is the side length of a square with area \(\frac{1}{16}\) square units?
3. What is the volume of a cube with edge lengths of \(\frac23\) units?
4. What is the edge length of a cube with volume \(\frac{27}{64}\) cubic units?

Select all the expressions that represent the area of the shaded rectangle.

\(3(10-c)\)

\(3(c-10)\)

\(10(c-3)\)

\(10(3-c)\)

\(30-3c\)

\(30-10c\)

A ticket at a movie theater costs $8.50. One night, the theater had $29,886 in ticket sales.

1. Estimate about how many tickets the theater sold. Explain your reasoning.

2. How many tickets did the theater sell? Explain your reasoning.

A fence is being built around a rectangular garden that is \(8 \frac{1}{2}\) feet by \(6 \frac{1}{3}\) feet. Fencing comes in panels. Each panel is \(\frac{2}{3}\) of a foot wide. How many panels are needed? Explain or show your reasoning.